Get Max Alternating Music

In a binary string you may flip one character at a time, at most k times. Find the maximum length of a contiguous substring in which every pair of adjacent characters differs. It is a substring, not a subsequence, and flips apply to single characters, not to whole ranges.

输入格式

The first line contains the binary string; the second line contains k. This site uses 1≤length≤200000, 0≤k≤200000.

输出格式

Output a single integer, the answer.

样例 1

输入：

0000
1

输出：

3

样例 2

输入：

01010
0

输出：

5

样例 3

输入：

111
2

输出：

3

样例说明

The answers are 3, 5 and 3.